The Reds rejected three offers from Barcelona for Coutinho during the summer transfer window, and the Brazilian recently claimed that he is happy at Anfield.
Recent reports, however, have suggested that PSG are also interested in signing the 25-year-old.
"I talk a lot with Coutinho. I hope that at the end of the season or even before, it could be a nice surprise for us," Silva is quoted as saying by Telefoot.
"I hope he will think well and that next year he will work with us. As with Neymar, I give him a lot of advice. But I think the most important thing for him is to make the best decision."
Coutinho has scored five goals and created four more in 10 appearances for Liverpool across all competitions this season.